Q2:- Apply romberg's method to the integral of f(x) = nx*cos(-Tx to 2 with Tol = 10-4

Q: The integral 4x dx Vx2 – 4 1 is an improper integral of typel is an improper integral of type II…

A: The given problem is solved below in detail.

Q: Evaluate the double integral. LL. 3 (x² – xy2) dy dx -3

A: first, we integrate with respect to y

Q: Use Simpson’s Rule with n = 4 to approximate ∫1  ex^2dx

A: The given function is continuous on the interval [0, 1], then using Simpson’s rule to find the…

Q: determine whether the improper integral converges and, if so, evaluate it.

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Q: how I calculate the definate integral 3x^2-e^2x(dx) on the interval ln3 to 0

A: To find the definite integral

Q: The particular Integral for (D² + 19²)y = sin19z is Yp 38 O Yp 19 O None O Yp Zacon19z 38

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Q: Determine whether the improper integral converges and, if so, evaluate it.

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Q: Use the Midpoint Rule with n= 10 to approximate the integral integral 0 to 1 e x 2  Give an upper…

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Q: Evaluate the integral: Se3+ cosh2x33+ cosh2xsinh2x dx A (3e)3+ sinh2x 21n3 - + C (3e)3 + cosh2x B…

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Q: Find the indefinite integral. (Use C for the constant of integration.) 4 zV 64z2 dz 49

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Q: Determine whether the improper integral diverges or converges. dx 1.So (2x-1) 7 dx 2. x +1

A: We have to determine whether the improper integral ∫-17 dxx+1 diverges or converges.

Q: 2. Identify which of the following integrals are improper: 1 1 dx 1 fin(x)dx 1 X +3 1 fe* dr -dp- 3

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Q: 4) Use the Midpoint Rule to approximate the integral. Then evaluate the actual integral. L(3x - 7)²…

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Q: x³ + 6x2 + x+2 2 Tan Ve fx-1 ax + In{(x+ 1)*(x² – x + 1)"| + The resulting integral of -X+ -1 + C,…

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Q: –1 dx x V In (-x) -3

A: Find the type of the generalized integral and examine its convergence.…

Q: Compute the value of the following improper integral. If it converges, enter its value. Enter…

A: The given integral is: I=∫2∞dx(2x-2)2 Substitute 2x-2=u⇒2dx=du⇒dx=du2As x→2⇒u→2as x→∞⇒u→∞ Therefore,…

Q: x-3 dx r³+9x +9.x

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Q: =dx V2x* +3 4

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Q: The improper integral J dx converges to x-5 4 о попе 1

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Q: Evaluate the integral. (Use C for the constant of integration.) te-8t dt

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Q: determine whether the improper integral converges and, if so, evaluate it.

A: To evaluate:

Q: Evaluate the integral –4x3/2 In(x) dx, x >0 Note: Use an upper-case "C" for the constant of…

A: Evaluate the integral

Q: Find the general indefinite integral. (Use C for the constant of integration.) ∫3v(v2+4)2dx

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Q: Evaluate the integral. (Use C for the constant of integration.) х dx x2 + x + 3

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Q: 1. Find the values of the following improper integrals with unbounded domains of integration, if…

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Q: At the point of discontinuity on(0, 00), the Fourier Sine integral converges to: OA None f(x+) -…

A: Here  At the point of discontinuity on  0,∞ the Fourier sine integral converges to

Q: Estimate the errors in the approximations for T10 and M10 of the integral from 1 to 2 of e1/x dx,…

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Q: Evaluate the integrals that converge: 3 dx 2x ! b) | a) dx (x² + 5)³ 3 – x -00

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Q: 2x (г — 1)2(2?2 + 1)

A: In this question, the concept of Integration is applied. Integration Integration is a method of…

Q: 1 Evaluate the double integral by reversing the order of integration 3* sin(xy?) dydx

A: First, we will change the order of integration then we will solve it.

Q: Use Simpson rule' 1/3 Method with (n = 8) to estimate the integral: f(x) : e^(sin 9x), where a = 0 &…

A: Given; f(x) = e^(sin 9x) and n=8 And a=0 , b=10

Q: If f(x)dx - + what are the bounds of integration for the first integral? a = and %3D

A: To find the bounds of integration

Q: Approximate the integral from 3 to -3 of (2+x2) dx using five equal subintervals.

A: We have to divide -3 to 3 into five equal subintervals.Length from -3 to 3 is 3 - (-3) =6So length…

Q: When using Simpson's rule to approximate the integral In(x+1)dx, then the upper bound of the error…

A: Consider the given information. I=∫23lnx+1dx Let's take 1 for n for the error bound. Calculate the…

Q: determine whether the improper integral converges and, if so, evaluate it.

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Q: 22. Detemine whether the improper integral converges or diverges, and if it converges, find its…

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Q: Compute the approximation  of the integral -4 to 4 e^(-x^2) using the trapezoid rule with n=4; you…

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Q: 13. Find the integral using the u substitution method Jx(x+1)*dx

A: Solution of question as follow

Q: Evaluate the integral. (Use C for the constant of integration.) 11 dx x²V 4x² - 1

A: Given integral ∫11dxx24x2-1=11∫dxx24x2-1 Now consider ∫dxx24x2-1 Use substitution method to solve…

Q: Evaluate the integral. (Use C for the constant of integration.) x² - 36 dx v3

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Q: Use Simpson’s Rule with n = 4 to approximate ∫1  ex^2dx 0   (integral from 0 to 1 of e^x^2 dx)

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Q: J. xinx) dx converges and evaluate the integral in those cases. Determine for what values of p the…

A: Consider the equation

Q: How many times do you need to integrate by parts to reduce ff(In x)° dx to an integral of In x? ·

A: Given integral is ∫1eln x6dx

Q: - Prove using integrals Proper tos : e even sin()fc) dx=0 -b 9- For even functions.

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Q: determine whether the improper integral converges and, if so, evaluate it.

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Q: Evaluate the integral S - dx V16-x2

A: Evaluate the integral of the integrand  x2/√(x2-16) .

Q: 2. Evaluate the improper integral S₂ (5. dx (5-x)4/3 or state that it diverges.

A: The given integral,      ∫28dx5-x43

Q: 3. Find the value of c guaranteed by the MVT for integrals for f(x) = cos(x), [-; 3'3 ] over this…

A: f(x)= cosx  , [ -π3,π3]as per MVT for Integrals for a function f(x) bounded and integrable on [a,b],…

Q: Calculate the integral approximation S6 for 2 2-a" dx. 1 S6

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Q: 4. Evaluate this integral by reversing the order of integration: Vy3 +1 dy dx.

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